Can continuous-time stationary stable processes have discrete linear representations?

We show that a non-trivial continuous-time strictly [alpha]-stable, [alpha][set membership, variant](0,2), stationary process cannot be represented in distribution as a discrete linear processwhere is a collection of deterministic functions and are independent strictly [alpha]-stable random variables. Analogous results hold for self-similar strictly [alpha]-stable processes and for strictly [alpha]-stable processes with stationary increments. As a consequence, the usual wavelet decomposition of Gaussian self-similar processes cannot be extended to the [alpha]-stable, [alpha]<2 case.